Question: What do the following two equations represent? $2x-y = 4$ $-6x+3y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x-y = 4$ $-y = -2x+4$ $y = 2x - 4$ Putting the second equation in $y = mx + b$ form gives: $-6x+3y = 5$ $3y = 6x+5$ $y = 2x + \dfrac{5}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.